A Rectangular Field Is to Be Enclosed on Four Sides $\$ 5$

A rectangular field is to be enclosed on four sides with a fence. Fencing costs $\$ 5$ per foot for two opposite sides, and $\$ 6$ per foot for the other two sides. Find the dimensions of the field of area $710 \mathrm{ft}^{2}$ that would be the cheapest to enclose. Round to the nearest tenth.

A) $22.2 \mathrm{ft} @ \$ 5$ by $32 \mathrm{ft} @ \$ 6$
B) $24.3 \mathrm{ft} @ \$ 5$ by $29.2 \mathrm{ft} @ \$ 6$
C) $29.2 \mathrm{ft} @ \$ 5$ by $24.3 \mathrm{ft} @ \$ 6$
D) $32 \mathrm{ft} @ \$ 5$ by $22.2 \mathrm{ft} @ \$ 6$